Optimal Multiplexed Hierarchical Modulation for Unequal Error Protection of Progressive Bit Streams

Optimal Multiplexed Hierarchical Modulation for Unequal Error Protection of Progressive Bit Streams Seok-Ho Chang†, Minjoong Rim‡, Pamela C. Cosman† and Laurence B. Milstein† †ECE Dept., University of California at San Diego, La Jolla, CA 92093, USA ‡ICE Dept., Dongguk University, Seoul, Korea Abstract—Progressive image and scalable video have gradual quality. Since these progressive transmissions have gradual differences of importance in their bitstreams, which can benefit differences of importance in their bitstreams, a large number from multiple levels of unequal error protection (UEP). Though of error protection levels are required. However, hierarchical hierarchical modulation has been intensively studied as an UEP approach for digital broadcasting and multimedia transmission, modulation can achieve only a limited number of UEP levels methods of achieving a large number of UEP levels have rarely for a given constellation size. For example, hierarchical 16 been studied. In this paper, we propose a multilevel UEP system QAM provides two levels of UEP, and hierarchical 64 QAM using multiplexed hierarchical quadrature amplitude modulation yields at most three levels [11]. In the DVB-T standard, video (QAM) for progressive transmission over mobile radio channels. data encoded by MPEG-2 consists of two different layers, We suggest a specific way of multiplexing, and prove that multiple levels of UEP are achieved by the suggested method. When and thus the use of hierarchical 16 or 64 QAM meets the the BER is dominated by the minimum Euclidian distance, we required number of UEP levels. However, if scalable video derive an optimal multiplexing approach which minimizes both is to be incorporated in a digital video broadcasting system, the average and peak powers. An asymmetric hierarchical QAM hierarchical 16 or 64 QAM may not meet the system needs. which reduces the peak-to-average power ratio (PAPR) without Most of the work about hierarchical modulation up to now performance loss is also proposed. Numerical results show that the performance of progressive transmission over Rayleigh fading has considered only two layered source coding, and to the channels is significantly enhanced by the proposed UEP systems. best of our knowledge, methods of achieving an arbitrarily large number of UEP levels have not been studied. I. INTRODUCTION In this paper, we propose a multilevel UEP system using When a communication system transmits messages over multiplexed hierarchical modulation for progressive transmis- mobile radio channels, they are subject to errors, in part be- sion over mobile radio channels. We propose a specific way cause mobile channels typically exhibit time-variant channel- of multiplexing, and prove that multiple levels of UEP are quality fluctuations. For two-way communication links, these achieved by the proposed method. These results are presented effects can be mitigated using adaptive methods. However, in Section II. When the BER is dominated by the minimum the adaptive schemes require a reliable feedback link from the Euclidian distance, we derive an optimal multiplexing ap- receiver to the transmitter. Moreover, for a one-way broadcast proach which minimizes both the average and peak powers, as system, those schemes are not appropriate because of the presented in Section III. While the suggested methods achieve nature of broadcasting. When adaptive schemes cannot be multilevel UEP, the PAPR typically will be increased when used, the way to ensure communications is to classify the data constellations having distinct minimum distances are time- into multiple classes with unequal error protection (UEP). multiplexed. To mitigate this effect, an asymmetric hierarchical Since the theoretical and conceptual basis for UEP was QAM constellation, which reduces the PAPR without perfor- initiated by Cover [1], much of the work has shown that mance loss, is proposed in Section IV. It is also shown that one method of achieving UEP is based on a constellation of asymmetric hierarchical QAM can provide multilevel UEP nonuniformly spaced signal points [2]–[5], which is called a even when multiplexed constellations need to have constant hierarchical constellation. In this constellation, more important power. In Section V, the performance of the suggested UEP bits in a symbol have larger minimum Euclidian distance than system for the transmission of progressive images is analyzed less important bits. Hierarchical constellations were intensively in terms of the expected distortion, and Section VI presents studied for digital broadcasting systems and multimedia trans- numerical results of performance analysis. mission [2][4]–[7]. Moreover, the Digital Video Broadcasting (DVB-T) standard [8], which is now commercially available, II. MULTILEVEL UEP BASED ON MULTIPLEXING incorporated hierarchical QAM for layered video data trans- HIERARCHICAL QAM CONSTELLATIONS mission. Progressive image and scalable video encoders [9][10], A. Hierarchical 16 QAM Constellation which are expected to have more prominence in the future, Fig. 1 shows a hierarchical 16 QAM constellation with employ a progressive mode of transmission such that as more Gray coded bit mapping [8]. The two most significant bits bits are transmitted, the source can be reconstructed with better (MSBs), i1 and q1, determine one of the four clusters, and 978-1-4244-4148-8/09/$25.00 ©2009 This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings. Data classes i1 00 11 Hierarchical i 2 01 10Cluster Channel 16 QAM Class 1 Encoder 1 (1) Hierarchical symbols q1 q2 (1) 16 QAM Constellation Average power 1 Mapper 1 Channel 0 0 Class 2 (5) Distance factor 1 Encoder 2 (2) d L 0 1 Channel Class 3 Encoder 3 (3) Hierarchical (2) 16 QAM d Constellation M Average power 2 Mapper 2 Channel Class 4 (6) Distance factor 2 Encoder 4 Less (4) Multiplexer 1 1 important Channel Class 5 Encoder 5 (5) Hierarchical (3) 16 QAM 1 0 Constellation Average power 3 Mapper 3 Channel Class 6 (7) Distance factor 3 Encoder 6 (6) d M d L Channel Class 7 Encoder 7 (7) Hierarchical (4) 16 QAM Constellation Average power 4 Mapper 4 Fig. 1. Hierarchical 16 QAM constellation. Channel Class 8 (8) Distance factor 4 Encoder 8 (8) their minimum Euclidian distance is dM . The two least sig- Fig. 2. The multilevel UEP system using multiplexed hierarchical 16 QAM nificant bits (LSBs), i2 and q2, determine which of the four constellations based on Theorem 1. signal points within the cluster is chosen, and their minimum Euclidian distance is d . The distance ratio α = d /d (> 1) L M L that 2N levels of UEP can be achieved by multiplexing N determines how much more the MSBs are protected against hierarchical 16 QAM constellations. errors than are the LSBs. Since hierarchical 16 QAM has one Theorem 1: For N hierarchical 16 QAM constellations, embedded QPSK subconstellation consisting of four clusters P and P , given by (3), satisfy and provides two levels of UEP, it is denoted by 4/16 QAM. M,i L,i We consider multiplexing N hierarchical 16 QAM constel- PM,1 <PM,2 < ···<PM,N <PL,1 <PL,2 < ···<PL,N lations. The average power per symbol of all the multiplexed (4) constellations, Savg, is given by for all SNR if N dM,1 >dM,2 > ···>dM,N >dL,1 >dL,2 > ···>dL,N . S 1 S avg = N avg,i (1) (5) i=1 Proof: The proof of this theorem as well as the proofs of all other results are not included here due to space limitations, where Savg,i is the average power per symbol of constellation but they can be found in [12]. i. Savg,i is given by Fig. 2 depicts the multilevel UEP system using multiplexed d 2 d 2 d2 hierarchical 16 QAM constellations based on Theorem 1 for S M,i M,i d M,i d d d2 avg,i = + + L,i = + M,i L,i+ L,i eight data classes (N =4). 2 2 2 2 (2) B.Hierarchical 2 K (K ≥ 3) QAM Constellation N 2K K ≥ where dM,i and dL,i are minimum distances for the MSBs and Next, we consider multiplexing hierarchical 2 ( i d ≤ n ≤ K LSBs of constellation , respectively. The BERs of the MSBs 3) QAM constellations. Let Mn,i (1 ) denote the and LSBs of hierarchical 16 QAM constellation i, denoted by minimum distance for the nth MSBs of constellation i (1 ≤ i ≤ N PM,i and PL,i, respectively, are given by [11] ). Theorem 2: If the SNR of interest for the nth MSBs d γ ≤ n ≤ K P 1Q M,i 2 s (2 ) is sufficiently large so that the probability of the M,i = d 1 d 2 2 Savg noise exceeding the Euclidian distance of Mn−1,i + 2 Mn,i is 1 insignificant compared to that of the noise exceeding dM ,i d γ 2 n 1 M,i 2 s (note that the distance ratio of the hierarchical constellation, + Q + dL,i 2 2 Savg d /d is greater than unity), the BER of the nth Mn−1,i Mn,i MSBs (2 ≤ n ≤ K), P , becomes d γ d γ Mn,i P Q L,i 2 s 1Q d L,i 2 s L,i = S + M,i + S P app = 2 avg 2 2 avg ⎧Mn,i − − 2K n−1 1 d K +2K q 2 ⎪ Q Mn,i p d γs d γ ⎪ =0 2K−n 2 + = +1 2K−q+1 M ,i −1Q d 3 L,i 2 s ⎪ p q n q Savg M,i + S (3) ⎨ ≤ n ≤ K − 2 2 avg for 2 1 d 2 1 d 2 (6) ⎪Q MK ,i γs Q d MK ,i γs ⎪ 2 + 2 MK−1,i + 2 where γs is the signal-to-noise ratio (SNR) per symbol, and ⎪ Savg Savg √ ∞ 2 ⎩⎪ Q x / π e−y /2dy n K ( )=1 2 x .

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